Articles https://doi.org/10.1038/s41567-019-0592-7
A laboratory model for the Parker spiral and magnetized stellar winds
Ethan E. Peterson 1*, Douglass A. Endrizzi 1, Matthew Beidler2,3, Kyle J. Bunkers 1, Michael Clark1, Jan Egedal1, Ken Flanagan 1, Karsten J. McCollam1, Jason Milhone 1, Joseph Olson 1, Carl R. Sovinec 2, Roger Waleffe 1, John Wallace1 and Cary B. Forest1
Many rotating stars have magnetic fields that interact with the winds they produce. The Sun is no exception. The interaction between the Sun’s magnetic field and the solar wind gives rise to the heliospheric magnetic field—a spiralling magnetic struc- ture, known as the Parker spiral, which pervades the Solar System. This magnetic field is critical for governing plasma processes that source the solar wind. Here, we report the creation of a laboratory model of the Parker spiral system based on a rapidly rotating plasma magnetosphere and the measurement of its global structure and dynamic behaviour. This laboratory system exhibits regions where the plasma flows evolve in a similar manner to many magnetized stellar winds. We observe the advec- tion of the magnetic field into an Archimedean spiral and the ejection of quasi-periodic plasma blobs into the stellar outflow, which mimics the observed plasmoids that fuel the slow solar wind. This process involves magnetic reconnection and can be modelled numerically by the inclusion of two-fluid effects in the simulation. The Parker spiral system mimicked in the labora- tory can be used for studying solar wind dynamics in a complementary fashion to conventional space missions such as NASA’s Parker Solar Probe mission.
n 1958, Eugene Parker first predicted the existence of the dominant plasma forces change in nature. These three interfaces supersonic solar wind1, which was subsequently verified by are the transonic, trans-Alfvénic and trans-β zones1,11,12. They char- Iearly spacecraft missions2,3. He also theorized how this solar acterize where the solar wind speed becomes supersonic, where it wind interacts with the dynamo-generated magnetic field of the becomes super-Alfvénic (inertial forces dominate magnetic forces, Sun—carrying the magnetic field lines away from the star, while that is VAlfven B=pμ0min
1Department of Physics, University of Wisconsin–Madison, Madison, WI, USA. 2Engineering Physics Department, University of Wisconsin–Madison, Madison, WI, USA. 3Present address: Oak Ridge National Laboratory, Oak Ridge, TN, USA. *e-mail: [email protected]
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a Virtual c Separatrix Anodes Helmholtz coil 3D Hall sensor array B cathode φ LaB6 cathodes 2D mach and triple probes
J φ JR
B φ
SmCo dipole
b 15 )
–1 10 VA
Vφ 5 V (km s VR Mo 0 anodes 0 0.2 0.4 0.6 0.8 R (m)
Fig. 1 | A laboratory recipe for creating a Parker spiral and stellar wind. a, Drawing current from anodes in the plasma atmosphere to a virtual cathode in the magnetosphere creates a cross field current JR and associated torque on the plasma. b, This torque drives plasma rotation, shown by the toroidal velocity Vφ (green solid line). The rotation becomes super-Alfvénic at the radius denoted by the star when the rotation speed surpasses the Alfvén speed,
VA (blue dash-dotted line). This super-Alfvénic rotation launches a radial wind shown by VR (orange dashed line). This wind then stretches the magnetic field lines outwards while they are twisted into a spiral by rapid rotation, forming the magnetic structures shown in a. This evolution produces a separatrix between the closed and open flux surfaces—a characteristic that is universal to many magnetized winds, and the understanding of which is vital to the study of stellar momentum transport and evolution. The experimental procedure to create the Parker spiral system is described in more detail in the Methods. c, Schematic of the experiment. relevant to the evolution of stellar winds, with special attention The remainder of this Article presents the measurements of this given to the dynamics near the Alfvén and β = 1 surfaces. laboratory Parker spiral, demonstrating three major findings: (1) In this Article, we report the creation of a laboratory model of the magnetic field is advected into an Archimedean spiral, (2) the the Parker spiral system and the measurement of its global struc- associated current sheet is dynamic and produces plasmoids near ture and dynamic behaviour. This system is realized by produc- the Alfvén radius, (3) these plasmoids travel outwards at super- ing a rotating plasma magnetosphere whose magnetic topology Alfvénic speeds and can be understood through the lens of Hall- evolves from a closed magnetosphere into an Archimedean spi- MHD. For comparison to the dynamics of the solar wind, Table 1 ral. We show that this system develops interface regions where outlines some dimensionless parameters relating this experiment in V ≈ VAlfvén and β ≈ 1, which become highly dynamic and result in the BRB to the solar wind. Although this laboratory system cannot processes that transport plasma from closed dipolar flux surfaces reflect the scale of the heliosphere, has no appreciable gravitational out to the open field lines of the Parker spiral. The experiments are effects, has a constrained return current path and does not produce compared to two-dimensional (2D) extended magnetohydrody- supersonic flows, it nevertheless recreates the macroscopic topology namic (MHD) simulations performed with the NIMROD code21, of stellar magnetic fields like the Parker spiral and its interactions which convincingly show that two-fluid (Hall) effects are essential with Alfvénic plasma flows. for understanding the current sheet and flows that develop. These We begin, for context, by summarizing the time dynamics of a experiments were carried out in the Big Red Ball (BRB) device at shot sequence as shown in Fig. 2. Important to note are the two the Wisconsin Plasma Physics Laboratory (WiPPL)22. The BRB, distinct phases present, which are characterized by an initial, non- shown in Fig. 1c, is a versatile 3-m-diameter multi-dipole con- axisymmetric state with large broadband fluctuations (phase I) and finement device capable of confining high-ionization-fraction, an axisymmetric, coherent, unstable state (phase II). A snapshot unmagnetized plasmas, and is well suited for investigations of basic of visible light captured by a fast camera during each of these two plasma systems and phenomena. phases shows non-axisymmetric density structures that follow the To create a rotating stellar wind in the laboratory, we use a dipole spiralling magnetic field in phase I (Fig. 2e) and a more diffuse, magnet similar to previous terella experiments23,24, but embed the axisymmetric density in phase II (Fig. 2f). Power spectral densities artificial magnetosphere in a much larger unmagnetized plasma of magnetic and density fluctuations in the current sheet during atmosphere. We then employ electromagnetic stirring techniques25,26 these two phases confirm the presence of coherent modes arising to produce rotation comparable to the Alfvén speed, as outlined in after a period of high-amplitude broadband fluctuations (Fig. 2d). Fig. 1b and described in detail in the Methods. When the plasma Although phase I exhibits interesting dynamics, in this study we rotation reaches the Alfvén speed, the centrifugal force of the wind focus on the mean field quantities and coherent modes during the overwhelms the magnetic confining force and the plasma can iner- axisymmetric phase II. tially break free from the magnetosphere, stretching and twisting Mapping out the time-resolved, 2D structure of the Parker spi- the magnetic field into a Parker spiral (Fig. 1a,c). ral is performed with linear arrays of three-axis Hall sensors, mach
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Table 1 | Dimensionless parameter comparison of the BRB and a 200 solar wind I II 100
Re Rm L/λe L/λi Ωceτe Ωciτi P (kW) 0 BRB 35 50 0.3 30 250 0.05 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Solar wind 20 1014 2 2 108 106 Time (s)
The Reynolds number Re is comparable in both cases, implying similar hydrodynamic behaviour. b
) 10
Both systems exhibit magnetic Reynolds numbers Rm 1, indicating low magnetic diffusivity –3 >> Te
as well as circumstances where momentum diffusion dominates magnetic diffusion, namely m ne
17 5 the magnetic Prandtl number Pm = Rm/Re > 1. The electron and ion collisionality, given by L/λe (eV) e T
and L/λi, respectively, expresses how many collisions a particle experiences as it transits across (10 e a system of size L, where λe and λi are the electron and ion mean free paths. One can see that n 0 electrons suffer a similar number of collisions in both systems. However, in the experiment the 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 ions are much more collisional than in the solar wind. The magnetization of electrons and ions Time (s) indicates how many gyro-orbits a particle undergoes before suffering a collision and is given by
Ωceτe and Ωciτi, where Ωce and Ωci are the electron and ion cyclotron frequencies, respectively, c 1.0 and τe and τi are characteristic electron and ion collision times. Therefore, the electrons are N pole highly magnetized in both systems, whereas the ions are only magnetized in the solar wind. The S pole 0.5 estimates of parameters for the BRB were made using a system size of L = 30 cm. Estimates for I (kA) the solar wind were made from fits to spacecraft data in the ecliptic plane27 and were taken at 5R , using L 5R . In summary, both systems demonstrate relatively collisionless, magnetized 0 ¼ 0.4 0.6 0.8 1.2 1.4 1.8 2.0 electronsI withI Rm >> 1 and Pm > 1. However, the ions in the BRB are neither collisionless nor 1.0 1.6 magnetized. Time (s) d 10–4
10–5 probes and triple probes. The resulting measurements of the mag- netic field structure and comparison to simulations are provided in 10–6
Fig. 3. Figure 3a shows that the contours of the poloidal magnetic 10–7 BZ (Phase I) flux (black lines) form an elongated magnetosphere. This figure also PSD (a.u.) Isat (Phase I) 10–8 shows antiparallel toroidal magnetic fields above and below the cur- BZ (Phase II) I (Phase II) rent sheet (cyan dashed line), with an up–down asymmetry caused sat 10–9 by preferential current drawn to an anode below the equator in the 103 104 105 plasma atmosphere. The data shown in Fig. 3a are compared to Frequency (Hz) MHD and Hall-MHD simulations (Fig. 3c,d). The Hall case shows e f closer agreement to the data as more magnetic flux is expelled from Phase I Phase II the magnetosphere (Fig. 3b), leading to higher values of β and larger magnetic curvature in the current sheet. An axisymmetric 3D ren- dering of field lines from data measured by magnetic probes reveals the Parker spiral topology with antiparallel toroidal fields above and below the closed field region (Fig. 3e). In addition to the magnetic structures, the plasma flows were measured and similarly compared to the aforementioned NIMROD simulations in Fig. 4. The results confirm that the toroidal flow in the experiment approaches the Alfvén speed in the current sheet with a peak at Alfvén radius RAlfvén = 30 cm, shown in Fig. 4b. From Fig. 4b it is also clear that the rotation becomes super-Alfvénic in the MHD simulation (Fig. 4c), whereas rotation in the Hall-MHD Fig. 2 | Magnetospheric evolution exhibits two distinct phases. An initial model (Fig. 4d) is limited to MAlfvén ≈ 1 and is consistent with the period of large-amplitude, non-axisymmetric, broadband fluctuations experiment. The mean radial flow along the current sheet in the is followed by a quiescent, axisymmetric, coherent instability. a–c, Time experiment was measured to be indistinguishable from zero and is dynamics of LaB6 cathode input power (P) (a), electron temperature (Te) once again in closer agreement with the Hall-MHD model, which and density (ne) (b) and polar cathode current injection (I) at both the produces a weakly accreting magnetosphere rather than a radial north (N) and south (S) poles of the dipole magnet (c) show the duration wind as in the MHD simulation. The experiment succeeded in cre- of these two phases denoted by the different hatched regions. d, Power ating a rapidly rotating magnetosphere with peaked rotation rates spectral densities (PSDs) for magnetic field BZ and density fluctuations comparable to the local Alfvén speed. It is important to note that computed from ion saturation current Isat measurements, with higher levels the peak in the MAlfvén profile occurs around R = 30 cm, which corre- during phase I and coherent modes arising later in phase II. a.u., arbitrary sponds to the location where magnetic reconnection and plasmoid units. e,f, Visible light emission imaged with a Phantom camera is shown formation take place. for non-axisymmetric (e, phase I) and axisymmetric (f, phase II) periods. The 2D reconstruction of the magnetic fluctuations was per- Error bars indicate s.d. for the full ensemble of shots as a measure of shot formed using amplitude and phase correlations with a fixed reference to shot reproducibility. magnetic probe displaced 100° toroidally from the swept probe. The correlations confirmed the fluctuations to be axisymmetric, cor- roborating the video evidence of axisymmetric ‘strobing’ of visible which shows that plasmoids are ejected into the current sheet with light emission present near the end of Supplementary Video 1. This higher densities than the ambient plasma by ~10%. Interestingly, reconstruction revealed a periodic reconnection process occuring when compared to simulations, the Hall-MHD model produced near the Alfvén radius, which releases plasmoids into the current plasmoids of remarkably similar frequency to the experiment at sheet at a frequency of 20 kHz. The resulting time dynamics of the 15 kHz (Supplementary Video 3), whereas the MHD case produced plasmoid ejection process are shown in Supplementary Video 2, none. Tracking the propagation speed of plasmoids in both the
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RB (10−5 Wb m–1) φ
−15 −10 −5 0 5 10 15 a b 102 e Exp. data (a) 20 Vacuum data (a) B > 0 MHD (c) φ 101 B < 0 Hall-MHD (d) φ 0 B (G) Z (cm) 100
−20 β = 0.1 β = 1 β = 10 10–1 c d
20 20
0 0 Z (cm) Z (cm)
−20 −20 β = 0.1 β = 1 β = 10 β = 0.1 β = 1 β = 10 0 20 40 60 80 0 20 40 60 80 R (cm) R (cm)
Fig. 3 | Measured and simulated 3D magnetic fields result in a Parker spiral. Black contour lines show the in-plane (poloidal) magnetic flux, whereas the colour contours represent the out-of-plane (toroidal) magnetic field multiplied by cylindrical radius R. a,c,d, Magenta contours show the β = 0.1, 1, 10 surfaces and demonstrate that the experiment and Hall-MHD simulation expel more flux from the helmet streamer than in the MHD case. b, This is corroborated by radial profiles of the poloidal field strength before the plasma, given by the vacuum data, and during the experiment and simulations. These radial profiles are taken along the current sheet denoted by the cyan dashed line in a and Z = 0 in c and d. Error bars in b represent s.d. error estimates in the measured magnetic field along the current sheet. e, Axisymmetric rendering of the Parker spiral obtained by integrating the field line equations using magnetic probe measurements at one toroidal angle. This 3D structure is then repeated an arbitrary number of times to give the reader a sense of the measured Parker spiral’s axisymmetric nature. The colour scheme applied to this rendering is red for open field lines with Bφ > 0, blue for open field lines with Bφ < 0 and white for the closed field lines.
|V | (km s–1) φ
0 2 4 6 8 10 a b 101 20 Plasmoid VR 100
0 Alfvén M Z (cm) –1 10 Exp. data (a) −20 MHD (c) Hall-MHD (d) 10–2 0 20 40 60 80 0 20 40 60 80 R (cm) R (cm) c d 20 20
0 0 Z (cm) Z (cm)
−20 −20
0 20 40 60 80 0 20 40 60 80 R (cm) R (cm)
Fig. 4 | Measured rotation approaches the Alfvén speed along the current sheet. a,c,d, Measurements of toroidal rotation speeds Vφ are shown in a and compared to MHD (c) and Hall-MHD simulations (d). Blue contour lines with arrows in c and d depict streamlines of the poloidal plasma flow in the MHD and Hall-MHD simulations, respectively. b, The Hall-MHD case shows much slower rotation, but also expels more magnetic flux such that the flow is still marginally Alfvénic (orange dashed line). However, the radial flow is small and directed inward in the Hall-MHD simulation, forming a weakly accreting magnetosphere. The cyan data points represent profile measurements of toroidal ion flow along the current sheet (cyan dashed line in a) normalized to the local Alfvén speed. This shows a peak in the Alfvén mach number profile of MAlfvén = 0.8 ± 0.2 (error bars indicate s.d. error estimates for MAlfvén) at R = 30 cm. These data are compared to the toroidal velocity profiles along Z = 0 cm for the MHD and Hall-MHD models (likewise normalized to the local Alfvén speed). The red shaded region represents the range of plasmoid radial flow speeds as measured in the experiment.
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In summary, we have created a laboratory model of the Parker a 0.2 10 spiral and showed that it exhibits trans-β and trans-Alfvénic zones,
0.1 5 ñ much like many magnetized stellar winds. By creating a rapidly i (10 rotating plasma magnetosphere we stretch and twist the magnetic 0 0 16 m field into an Archimedean spiral, successfully mimicking the global Z (m) –3
) magnetic topology of the heliosphere. Doing so produces a dynamic –0.1 –5 interface region between closed field lines of the magnetosphere –0.2 –10 and the open field lines of the Parker spiral, forming a current sheet 0 0.2 0.4 0.6 0.8 1.0 and a ‘Y’-point. R (m) At this interface between closed and open magnetic fields, the toroidal current and poloidal magnetic field produce an inward b 0.2 10 directed electric field via the Hall effect. This electric field acts to 4 × 0.1 5 draw ions inward while accelerating electrons outward. As the ion ñ
i density builds up in the closed field region it causes the magnetic (10 0 0 field to balloon outward into the current sheet until the field can 16 Z (m) m reconnect, ejecting plasmoids with enhanced density into the out- –0.1 –5 –3 ) flow. These quasi-periodic plasmoids are observed in our experi- ment and mimic the observed plasmoids ejected from the tips of –0.2 –10 0 0.2 0.4 0.6 0.8 1.0 helmet streamers that fuel the slow solar wind. R (m) This experiment demonstrates that laboratory facilities possess abilities complementary to in situ spacecraft missions and are capa- Fig. 5 | Plasmoid ejection occurs in both the experiment and Hall-MHD ble of studying a wide range of physical phenomena relevant to the simulation. Pressure enhancement in the interior closed flux region origin and evolution of magnetized stellar winds. causes field lines inside the ‘Y’-point to balloon outward—stretching and eventually reconnecting to eject plasmoids. Videos of the experimental Online content plasmoids and Hall-MHD simulation plasmoids are provided in Any methods, additional references, Nature Research reporting Supplementary Videos 2 and 3, respectively. These videos show the summaries, source data, statements of code and data availability and experimental plasmoids to have velocities of 5–10 km s−1 as they travel associated accession codes are available at https://doi.org/10.1038/ from the Alfvén surface at R = 30 cm to R = 60 cm. Over this distance, the s41567-019-0592-7. local Alfvén speed drops from 4 km s−1 to 2 km s−1, giving these plasmoids an Alfvén mach number range of 1–5. The Hall-MHD simulation plasmoid Received: 20 March 2019; Accepted: 12 June 2019; velocities agree well with the experimental measurements at 6–8 km s−1. Published: xx xx xxxx
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Methods signals can be pulled from the trees, averaged over a given period (500 μs in this Producing an unmagnetized plasma atmosphere. To produce a steady-state analysis) and plotted. To calculate absolute velocity measurements, mach probe plasma atmosphere in the BRB, we start by pufng a small amount of helium into theory is used to compute the sonic mach number from the ratio of ion saturation the 3-m-diameter vacuum vessel using piezoelectric valves. Tis raises the pressure current measured by pairs of oppositely facing electrodes. The plasma sound speed in the vessel from 7 × 10−7 torr to ~5 × 10−5 torr, at which point we apply a voltage is calculated from measurements of the electron temperature by triple probes under the assumptions of cold ions and Z 1; these assumptions are justifiable between −200 V and −400 V to fve LaB6 thermionic cathodes with respect to many eff = grounded anodes. Tis ionizes the helium and produces a plasma. Te multi- in helium plasmas with these parameters and 100 kW of input power. The sound dipole confnement scheme of the BRB provides good confnement for this plasma, speed multiplied by the sonic mach number gives the results presented in Fig. 4a. allowing it to reach an electron temperature of 6.5 eV, density of 4 × 1017 m−3 and To compute the local Alfvén speed, the magnetic field data are interpolated onto an ionization fraction of ~25% with an input power of 100 kW for 1.5 s (Fig. 2a,b). the coarser-resolution density measurements. This is then used to normalize the Tis plasma then difuses into the dipole magnetic feld of the SmCo magnet that flow speed to obtain measurements of the Alfvén mach number. is placed at the centre of the BRB, providing the base plasma for driving a rotating To produce the plasmoid videos, we considered the time period of the shot magnetosphere immersed in an ambient plasma atmosphere. with the highest correlation across all shots, which turned out to be ~t = 1.125 s. In this time window, the dominant frequency is 20 kHz. Performing a form of Driving a rotating magnetosphere. To force rotation, we drive cross-field currents conditional averaging based on the mean and fluctuating levels of the stationary into the magnetosphere, exerting a torque on the plasma. The SmCo magnet has reference probe, windows of 500 μs are aligned in time on a shot to shot basis to two 3-inch-thin disk molybdenum electrodes fitted near its poles and attached build up a 2D map of the magnetic field dynamics. The same technique is used to conductors that carry the current they draw out along the axis of symmetry of with ion saturation current probes to show the phase relationship between density the machine. Only a small portion of the outer rim of each electrode is exposed to and magnetic field. What this reveals is that magnetic reconnection produces plasma, creating a virtual cathode flux tube along the field lines that connect the plasmoids that contain higher density than the surrounding plasma, as shown in electrodes, as shown in Fig. 1a. During the steady-state portion of the discharge, we Supplementary Video 2. Plasmoid velocities were computed from the videos by apply a −1 kV bias to each electrode with a 56 mF capacitor bank and 1.8 Ω resistor tracking the ‘O’-point of the magnetic islands as they travel outwards. producing a decaying current profile with a peak of ~500 A and τ = RC = 100 ms (Fig. 2c). The current going into the magnetosphere comes from grounded anodes NIMROD simulations. NIMROD is an extended-MHD code that uses 2D in the plasma atmosphere and therefore must cross many field lines to get to the finite element calculations and a Fourier series decomposition in the direction polar electrodes and be extracted. These cross-field currents yield a J × B torque on of symmetry to solve the MHD equations. The simulations discussed in this the plasma, causing it to rotate. Article were axisymmetric and were performed on a grid of quadrilateral elements resembling a 1.5-m-radius sphere with a 5-cm-radius cylinder removed around Data acquisition. Most of the data presented in this Article were produced R = 0 to allow space for the dipole magnet at the centre of the BRB (resembling by linear probe arrays mounted on 2D motorized stages. These stages allowed a cored apple). Both the MHD simulation and Hall-MHD simulation were 17 −3 for scanning in a poloidal plane to build up maps of the 2D time dynamics in performed with experimentally similar parameters of ne = 4 × 10 m , Te = 7 eV 2 −1 the magnetosphere at a given toroidal angle. One scan was performed with a and Ti ≈ 0.5 eV, which gives viscous and resistive diffusivities of ν ≈ 50 m s and 2 1 15-position three-axis Hall sensor array (to measure the magnetic field and η ≈ 30 m s− . The effects of neutral particles are included in these simulations currents) and two were performed with a four-position 2D mach and triple through a momentum sink term due to charge exchange with ions. This acts as a drag on the flow, reducing peak flow speeds. No other ionization sources or sinks probe for measurements of Vφ, VR, ne and Te. During each of these scans, a fixed position reference array of magnetic probes was used to provide phase reference are modelled in these simulations, but are indeed present in the experiment. The measurements. The resolution of the magnetic maps is ~3 cm and for the flow most important difference is the effect of ionization on the virtual cathode flux maps is ~4 cm. The Hall sensing integrated circuits used (part no. MLX91205KDC- tube, which would act to enhance the density in the magnetosphere and increase AAL) have a bandwidth of 100 kHz, and were used in a differential output the pressure gradient drive for the plasmoid ejection. The only difference between configuration. The signal from each chip was sent directly via twisted pair to the two simulations is the addition of the Hall and electron pressure gradient differential input digitizers (D-TACQ Solutions ACQ-196). These digitizers terms in Ohm’s law. Each simulation advanced the MHD equations starting from a sampled the magnetic signals at 200 kHz and directly uploaded raw voltage signals uniform density and temperature plasma with a dipole magnetic field and a small to MDSplus after each shot. The triple probe and mach probe signals were isolated vertical field to model the axisymmetric (with respect to the machine symmetry) and filtered before digitization by unity gain isolation amplifiers and third-order component of Earth’s field. During the advance, the current injection used to spin Bessel filters with a 3 dB point at 100 kHz. Each mach probe face was biased at the plasma is prescribed by specifying Bφ on the boundary of the simulation. In −120 V with respect to the machine wall (ground). This ensured that the mach all cases the current injection ramps up to a steady-state value in 1 ms and is held probe faces always collected ion saturation current. The 2D maps were built constant for the remainder of the simulation. up in a matter of hours, by taking 2–3 shots at each location at a 3 min repetition rate to allow for the capacitor banks to charge and the molybdenum electrodes to Data availability cool down. Raw data were generated at the Big Red Ball facility at the Wisconsin Plasma Physics Laboratory. Derived data supporting the findings of this study are available Data analysis. All of the data taken at the BRB are stored in a hierarchical data from the corresponding author upon reasonable request. tree structure by a software used frequently in the nuclear fusion community called MDSplus. MDSplus trees store probe positions, raw signals, calibration information and error calculations on a shot by shot basis, allowing for much of Code availability the signal processing chain to be stored in these trees using relational references Information about the NIMROD code, including publications and licensing and automated scripts. This means that to build the 2D maps shown in Figs. 3 and policies, is available at https://nimrodteam.org. Code produced for analysing 4, all that is required is a database of shots for a particular map and the desired data at the Big Red Ball Facility is available from the corresponding author upon time average interval. With this information, all the probe locations and associated reasonable request.
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